Sagemaker Studio: Amazon Q sign-in page/left side tab option not launching

## Problem
When we try to use Amazon Q extension in Amazon Sagemaker Studio Code editor, we are unable to see/launch the sign-in page/sidebar menu while clicking on the Amazon Q sign in pop-up.

## Steps to reproduce the issue
1. Open AWS console. Then navigate to Sagemaker Studio
2. Launch Sagemaker Studio Code editior
3. Open left sidebar, click on extensions
4. Then search for Amazon Q and try installing the extension
5. Once installed we can see a pop up on right bottom for sign-in
6. If we click on that we are not redirected to sign-in screen and the process or sign-in gets terminated

## Expected behavior
On Step 6 it should redirect to the sign-in page and let us sign-in either using AWS Builder id or By using a Pro license

## Workaround
Try Disabling the AWS Toolkit extension and then try to reload the page and you would be able to use the Amazon Q extension without any issue

## System details

- OS: Any (using Amazon Sagemaker Studio Code editor)
- Visual Studio Code version: Version: 1.83.1
- AWS Toolkit version: v3.23.0
- Amazon Q version: v1.24.0

Reproduce the flow in the SageMaker Studio Code editor using the listed AWS Toolkit and Amazon Q versions, starting from the Amazon Q sign-in popup after extension installation. Compare the behavior with the AWS Toolkit extension disabled and trace the interaction between the two extensions; done means the popup reliably opens the Builder ID or Pro license sign-in page.

Written by the indexing model from the issue text.